# Properties

 Label 139650.jb Number of curves $2$ Conductor $139650$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("jb1")

sage: E.isogeny_class()

## Elliptic curves in class 139650.jb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
139650.jb1 139650ck1 $$[1, 0, 0, -12983188, -31668533758]$$ $$-131661708271504489/159475479581250$$ $$-293158292144601269531250$$ $$[]$$ $$23224320$$ $$3.1966$$ $$\Gamma_0(N)$$-optimal
139650.jb2 139650ck2 $$[1, 0, 0, 109559687, 594629247617]$$ $$79116632600119361351/128876220703125000$$ $$-236908726398468017578125000$$ $$[]$$ $$69672960$$ $$3.7459$$

## Rank

sage: E.rank()

The elliptic curves in class 139650.jb have rank $$0$$.

## Complex multiplication

The elliptic curves in class 139650.jb do not have complex multiplication.

## Modular form 139650.2.a.jb

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} + q^{6} + q^{8} + q^{9} + 3 q^{11} + q^{12} + 5 q^{13} + q^{16} + 3 q^{17} + q^{18} - q^{19} + O(q^{20})$$

## Isogeny matrix

sage: E.isogeny_class().matrix()

The $$i,j$$ entry is the smallest degree of a cyclic isogeny between the $$i$$-th and $$j$$-th curve in the isogeny class, in the LMFDB numbering.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels.